Green’s Dictionary of Slang

sucky adj.1

also sucking
[suck n.1 ]

tipsy, slightly drunk.

[UK]B.E. Dict. Canting Crew n.p.: Suckey, drunkish, maudlin, half Seas o’er.
[UK]New Canting Dict. [as cit. c.1698].
[UK]Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
[UK]Proc. Old Bailey 23 Oct. 313/1: The prisoner told him he had it of a suckey cull, and Mr. Fielding said, Ben, what is the meaning of that word? his answer was, he could not tell.
[UK]Proc. Old Bailey 6 July 235/1: Said Craycraft, there is a sucking cull, that is, a drunken gentleman, go and ask him what he has got.
[UK]G. Parker View of Society II 105: The old woman having been used to get a little sucky now and then.
[UK] ‘Flash Lang.’ in Confessions of Thomas Mount 19: Drunk, sucky.
[UK]C.L. Lewes Comic Sketches 27: While others would say he [was], ‘Very much disguis'd — Clipp'd the King's English —Quite happy — Bosky—Fuddled — Muddled — Tipsy — Dizzy — Muzzy — Sucky’.
[UK]Lex. Balatronicum.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.